function urlencode (str) {
    // http://kevin.vanzonneveld.net
    // +   original by: Philip Peterson
    // +   improved by: Kevin van Zonneveld (http://kevin.vanzonneveld.net)
    // +      input by: AJ
    // +   improved by: Kevin van Zonneveld (http://kevin.vanzonneveld.net)
    // +   improved by: Brett Zamir (http://brett-zamir.me)
    // +   bugfixed by: Kevin van Zonneveld (http://kevin.vanzonneveld.net)
    // +      input by: travc
    // +      input by: Brett Zamir (http://brett-zamir.me)
    // +   bugfixed by: Kevin van Zonneveld (http://kevin.vanzonneveld.net)
    // +   improved by: Lars Fischer
    // +      input by: Ratheous
    // +      reimplemented by: Brett Zamir (http://brett-zamir.me)
    // +   bugfixed by: Joris
    // +      reimplemented by: Brett Zamir (http://brett-zamir.me)
    // %          note 1: This reflects PHP 5.3/6.0+ behavior
    // %        note 2: Please be aware that this function expects to encode into UTF-8 encoded strings, as found on
    // %        note 2: pages served as UTF-8
    // *     example 1: urlencode('Kevin van Zonneveld!');
    // *     returns 1: 'Kevin+van+Zonneveld%21'
    // *     example 2: urlencode('http://kevin.vanzonneveld.net/');
    // *     returns 2: 'http%3A%2F%2Fkevin.vanzonneveld.net%2F'
    // *     example 3: urlencode('http://www.google.nl/search?q=php.js&ie=utf-8&oe=utf-8&aq=t&rls=com.ubuntu:en-US:unofficial&client=firefox-a');
    // *     returns 3: 'http%3A%2F%2Fwww.google.nl%2Fsearch%3Fq%3Dphp.js%26ie%3Dutf-8%26oe%3Dutf-8%26aq%3Dt%26rls%3Dcom.ubuntu%3Aen-US%3Aunofficial%26client%3Dfirefox-a'
    str = (str + '').toString();

    // Tilde should be allowed unescaped in future versions of PHP (as reflected below), but if you want to reflect current
    // PHP behavior, you would need to add ".replace(/~/g, '%7E');" to the following.
    return encodeURIComponent(str).replace(/!/g, '%21').replace(/'/g, '%27').replace(/\(/g, '%28').
    replace(/\)/g, '%29').replace(/\*/g, '%2A').replace(/%20/g, '+');
}

Not our code, cribbed from the internet, authors accredited

Javascript equivilant of PHP's urlencode

JavaScript